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\begin_body
\begin_layout Title
Learning Topology and Geometry
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\begin_layout Subtitle
Automated Grammar Induction
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\begin_layout Author
Linas Vepstas
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\begin_layout Institute
AGI 2022
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\begin_layout Date
22 August 2022
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Learning Topology and Geometry
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A Lack of Topological and Geometric Awareness
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Critiques of DL/NN recently circulating on social media
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Learning Topology and Geometry
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\begin_deeper
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Conventional Simplical, Cellular Homology
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Triangulations, cycles, cocycles, universal covering groups, metrics
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Deep and broad mathemaical foundations to draw on.
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Learning Topology and Geometry
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Reframe: Edge Lists -> Jigsaws with Connectors
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Jigsaws, plus
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global
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constraints such as must-form-a-cycle
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Not quite graph theory.
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Not quite relational algebra.
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...
but almost so.
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Learning Topology and Geometry
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Connectors Indicate Symbolic Relationships
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Image segmentation as labelled geometric relationships
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Geometric syntax encodes part–whole relationships!
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Learning Topology and Geometry
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Jigsaw Paradigm Established in Linguistics
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Syntax in Link Grammar (1991) and earlier (Marcus, 1967)
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Maximum Spanning Tree parse from Word-Pair MI (1998)
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Learning Topology and Geometry
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Provides Semantics for Symbolic AI
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Abstract (Symbolic AI)
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Things that can be seen
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Syntax extending into shallow semantics
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Learning Topology and Geometry
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Not Just 1D, 2D, 3D, but also Abstract Sensory Domains
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Audio: frequency, intensity, time, envelope, chirp modulation
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More generally: wavelet-style decomposition
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Syntax and structure of a whale song
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Learning Topology and Geometry
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Segmentation and Tokenization as (evolutionary, ML) Program Learning
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Conventional ML/AI can explore DSP filter sequences
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Can DL/NN be used to generate these?
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Possibly ...
probably.
Not been done.
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Recursive...
(model->syntax->model->syntax...)
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...
and deep (
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cheap
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).
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Experimental results
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Gaussian Orthogonal Ensemble (Spin Glass)
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Uniform distribution of English word similarities in high dimensions.
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Conventional (information-theoretical) metrics apply.
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Common Sense as Inference over Symbolic Domains
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Enactive AI founded on unsupervised symbolic relationships.
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Common Sense
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can be learned recursively i.e.
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deeply
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.
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GOFAI failed because it depended on human-curated datasets.
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This proposal doesn't, but it remains (mostly) symbolic.
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GOFAI was shallow.
Shallow==hard-to-learn.
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